Jelly, 9 bytes
ÆEz0Ṣ€ZÆẸ
How it works
ÆEz0Ṣ€ZÆẸ Main link. Argument: A (array)
ÆE For each n in A, compute the exponents of n's prime factorization.
E.g., 2000000 = 273056 gets mapped to [7, 0, 6].
z0 Zip 0; append 0's to shorter exponent arrays to pad them to the same
length, then read the resulting matrix by columns.
Ṣ€ Sort the resulting arrays (exponents that correspond to the same prime).
Z Zip; read the resulting matrix by columns, re-grouping the exponents by
the integers they represent.
ÆẸ Unexponents; map the exponent arrays back to integers.
Jelly, 9 bytes
ÆEz0Ṣ€ZÆẸ
How it works
ÆEz0Ṣ€ZÆẸ Main link. Argument: A (array)
ÆE For each n in A, compute the exponents of n's prime factorization.
E.g., 2000000 = 273056 gets mapped to [7, 0, 6].
z0 Zip 0; append 0's to shorter exponent arrays to pad them to the same
length, then read the resulting matrix by columns.
Ṣ€ Sort the resulting arrays (exponents that correspond to the same prime).
Z Zip; read the resulting matrix by columns, re-grouping the exponents by
the integers they represent.
ÆẸ Unexponents; map the exponent arrays back to integers.